tomleslie

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9 years, 153 days

MaplePrimes Activity


These are answers submitted by tomleslie

at ?Grid, this package was introduced in Maple 15.

Note that is Maple 15 (released in 2011), not Maple 2015

The code

eqn:=a*x^3+b*x^2+c*x+d;
solve(eqn, x);

will return the solution of the general cubic.

In Maple the ratio of circle circumference to diameter is expressed by the name 'Pi' - note the capitalisation. The Greek letter 'pi', has no 'special' meaning - it is just a (Greek) name. So

sin(Pi/2) will automatically simplify to 1, and

sin(pi/2) cannot be evaluated to anything meaningful, so will just return unevaluated, is as sin(pi/2)

one of the two options shown in the attached?

  restart;

  interface(rtablesize=10):
  with(plots):

  colors:=[red, green, blue]:
  funcsToPlot:=[ sin(x), cos(x), sin(x)*cos(x)]:
  display
  ( [ seq
      ( plot
        ( funcsToPlot[j],
          x=-Pi..Pi,
          gridlines=false,
          color=colors[j],
          legend=convert(funcsToPlot[j], string),
          legendstyle=[font=[times, bold, 20]],
          size=[800,800]
        ),
        j=1..numelems(funcsToPlot)
      )
    ]
  );
  display
  ( [ seq
      ( plot
        ( funcsToPlot[j],
          x=-Pi..Pi,
          gridlines=false,
          color=colors[j],
          legend=cat("func", j),
          legendstyle=[font=[times, bold, 20]],
          size=[800,800]
        ),
        j=1..numelems(funcsToPlot)
      )
    ]
  );

 

 

 


 

Download legPlot.mw

@Stretto 

Simply replacing your 'piecewise()' statement with an equivalent(?) 'if()' statement seems to make the problem go away - and, NO, I don't know why!

With the latter, the fourier transforms for your two examples are successfully evaluated

See the attached

restart;

with(inttrans):
interface(rtablesize=10):
interface(version);

`Standard Worksheet Interface, Maple 2019.0, Windows 7, March 9 2019 Build ID 1384062`

(1)

sinc := x->`if`(x = 0, 1, sin(Pi*x)/x/Pi):
S := x->sinc(x):
fourier(S(x),x,s);
SE := x->sinc(x)*exp(-x^2):
fourier(SE(x),x,s);
plot(abs(fourier(S(x),x,s)),s=0..5);
plot(abs(fourier(SE(x),x,s)),s=0..5);

Heaviside(s+Pi)-Heaviside(s-Pi)

 

(1/2)*erf((1/2)*s+(1/2)*Pi)-(1/2)*erf((1/2)*s-(1/2)*Pi)

 

 

 

 

Download FT.mw

Deriving the recurrence relation from the actual numbers - tricky!

On the other hand - chect!

If you just want to know what the recurrence relation is, you can generate the first few numbers, then load these into the search box at oeis.org to see if you get a match. This came up with the Jacobsthal (who (s)he?) sequence ( A001045 ) and its recurrence relation

The attached shows how to generate the sequence the hard way by enumerating all the possible combinations and counting them, followed by calculating the recurrence relation for the (offset) Jacobsthal sequence given by oeis.org

  restart;

  interface(version);
  Physics:-Version();
  interface(rtablesize=10):

`Standard Worksheet Interface, Maple 2019.0, Windows 7, March 9 2019 Build ID 1384062`

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple", `2019, April 26, 7:48 hours, version in the MapleCloud: 353, version installed in this computer: 350.`

(1)

  with(combinat):
  with(StringTools):
  seq
  ( numelems
    ( remove
      ( i-> RegMatch("00|22|02|20", i),
        Implode~( permute
                  ( ["0"$j, "1"$j, "2"$j],
                    j
                  )
                )
      )
    ),
    j=0..10
  );

1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365

(2)

  a:=proc(n)
          option remember;
          if   n=0
          then return 0
          elif n=1
          then return 1;
          else return a(n-1)+2*a(n-2);
          fi;
    end proc:
 seq( a(j), j=2..12);

1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365

(3)

 


 

Download jacobs.mw

Sorry it took you a couple of days. The attached took me slightly less than a minute and *appears* to be correct.

Exactly what were you calculating? Please post worksheet showing problem

restart;

interface(version);
Physics:-Version();
interface(rtablesize=10):

`Standard Worksheet Interface, Maple 2019.0, Windows 7, March 9 2019 Build ID 1384062`

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple", `2019, April 26, 7:48 hours, version in the MapleCloud: 353, version installed in this computer: 350.`

(1)

restart;
with(Student[MultivariateCalculus]):
f:=(x, y) ->x^2-y^2;
Jacobian([f(x,y),f(x,y)],[x,y]);

f := proc (x, y) options operator, arrow; x^2-y^2 end proc

 

Matrix(%id = 18446744074382092998)

(2)

restart;
with(VectorCalculus):
f:=(x, y) ->x^2-y^2;
Jacobian([f(x,y),f(x,y)],[x,y]);

f := proc (x, y) options operator, arrow; x^2-y^2 end proc

 

Matrix(%id = 18446744074379823574)

(3)

 


 

Download jaco.mw

  1. while   (Norm(g(v0)) > 1e-6) do;   The function g() is undefined, so g(v0) wont evaluate to anything meaningful
  2. d0=-H0*g0, Should be  d0:=-H0*g0    (ie assigment not equality), but since H0is a 2X2 matrx and g0 is a 4X1 vector, this multiplication cannot be performed    

You just need to extend (and/or customize) the method shown in the attached

Output plot window+slider not appearing here, but does in worksheet (honest!)

  restart;

  interface(rtablesize=10):
  f:= proc(b)
           local sys:={ diff(x(t), t) = a*t, x(0)=0 },
                 sol:= dsolve(sys, numeric, parameters=[a]);
           sol(parameters=[b]):
           return plots:-odeplot( sol, [t, x(t)], t=0..1, view=[0..1, 0..3]);
      end proc:

  Explore( plots:-display(f(a)), parameters=[a=1..5]);

 

 


 

Download dsolExpl.mw

but, there are easier ways!

See the attached where I contrast your 'explicit' method with the built-in function composition operator

  retart

retart

(1)

  interface(rtablesize=10):

#
# As a test case, suppose the function 'F()'
#  is defined by - this could be anything
# ( which acceptsa possibly complex argument)
#
  F:=x->x^3;

proc (x) options operator, arrow; x^3 end proc

(2)

#
# OP's way to do repeated function application
#
  App := proc (k, z0)
               local z1, z2, j;
               z1 := z0;
               z2 := NULL;
               for j to k do
                   z2 := F(z1);
                   z1 := z2;
               end do;
               return z2;
         end proc:
  App(3, a+I*b);
  App(3, 1+2*I);

(a+I*b)^27

 

130656229-2726446322*I

(3)

#
# Less complicated way to do the same thing
#
  (F@@3)(a+I*b);
  (F@@3)(1+2*I);

(a+I*b)^27

 

130656229-2726446322*I

(4)

 


 

Download fcomp.mw

which I have fixed in the attached

  restart:

  interface(rtablesize=10):

#
# Define gamma as local (don't like doing this!)
#
  local gamma:local pi:
#
# Replaced 'indexed' parameters with 'inert subscript'
# parameters - otherwise one gets a problem defining
# both the unindexed 'phi' and the indexed phi[c]
#
  M__h := 100: beta__o := 0.034: beta__j := .025: mu__1 := 0.0004:
  epsilon := .7902: alpha := 0.11: psi := 0.000136: phi := 0.05:
  omega := .7: eta := .134: delta := .245: f := 0.21:
  M__v := 1000: beta__k := 0.09:   mu__v := .0005: M__c := .636:
  beta__g := 0.15: mu__c := 0.0019: pi :=0.01231: theta := 0.12: mu__e := 0.005:
#
# D() is Maple's differential operator replated D(T)
# with DD(T) in the following to avoid confusion
#
  ODE1 := diff(B(T), T) = M__h-beta__o*B(T)-beta__j*B(T)-mu__1*B(T)+epsilon*G(T)+alpha*F(T):
  ODE2 := diff(C(T), T) = beta__o*B(T)*J(T)-beta__j*C(T)-(psi+mu__1+phi)*C(T):
  ODE3 := diff(DD(T), T) = beta__j*B(T)*L(T)- beta__o*E(T)-(omega+mu__1+eta)*DD(T):
  ODE4 := diff(E(T), T) = beta__o*E(T)-beta__j*C(T)-(delta+mu__1+eta+phi)*E(T):
  ODE5 := diff(F(T), T) = psi*C(T)-(alpha+mu__1)*F(T)+f*delta*E(T):
  ODE6 := diff(G(T), T) = omega*DD(T)-(epsilon+mu__1)*G(T)+(1-f)*delta*E(T):
  ODE7 := diff(H(T), T) = M__v-beta__k*H(T)-mu__v*H(T):
  ODE8 := diff(J(T), T) = beta__k*H(T)-mu__v*J(T):
  ODE9 := diff(K(T), T) = M__c-beta__g*K(T)-mu__c*K(T):
  ODE10:= diff(L(T), T) = beta__g*K(T)-mu__c*L(T):
  ODE11:= diff(M(T), T) = pi*(DD(T)+ theta*E(T))-mu__e*M(T):

  B0 := 100: C0 := 90: D0 := 45: E0 := 38:
  F0 := 10: G0 := 45: H0 := 50: J0 := 70: K0 :=20: L0:= 65: M0 :=22:
#
# Solve system
#
  ans := dsolve( { ODE1, ODE2, ODE3, ODE4, ODE5, ODE6, ODE7, ODE8, ODE9, ODE10, ODE11,
                   B(0) = B0, C(0) = C0, DD(0) = D0, E(0) = E0,
                   F(0) = F0, G(0) = G0, H(0) = H0, J(0) = J0, K(0) = K0, L(0) = L0, M(0) = M0
                 },
                 numeric
               );
#
# Plot solutions for a few of the dependent variablss
# just to show everything is working (more-or-less!)
#
  plots:-odeplot( ans, [T, B(T)], T=0..5);
  plots:-odeplot( ans, [T, C(T)], T=0..5);
  plots:-odeplot( ans, [T, DD(T)], T=0..5);
  plots:-odeplot( ans, [T, E(T)], T=0..5);
  plots:-odeplot( ans, [T, F(T)], T=0..5);
  plots:-odeplot( ans, [T, G(T)], T=0..5);
  plots:-odeplot( ans, [T, H(T)], T=0..5);
  plots:-odeplot( ans, [T, J(T)], T=0..5);
  plots:-odeplot( ans, [T, K(T)], T=0..5);
  plots:-odeplot( ans, [T, L(T)], T=0..5);
  plots:-odeplot( ans, [T, M(T)], T=0..5);

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 11, (2) = 11, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.2540372220976533e-2, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..11, {(1) = 100.0, (2) = 90.0, (3) = 45.0, (4) = 38.0, (5) = 10.0, (6) = 45.0, (7) = 50.0, (8) = 70.0, (9) = 20.0, (10) = 65.0, (11) = 22.0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..11, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1, (9) = .1, (10) = .1, (11) = .1}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, 1..11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0}, datatype = float[8], order = C_order), Array(1..11, 1..11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, 1..11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0}, datatype = float[8], order = C_order), Array(1..11, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0}, datatype = integer[8]), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..22, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..11, {(1) = 100.0, (2) = 90.0, (3) = 45.0, (4) = 38.0, (5) = 10.0, (6) = 45.0, (7) = 50.0, (8) = 70.0, (9) = 20.0, (10) = 65.0, (11) = 22.0}, datatype = float[8], order = C_order), Array(1..11, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0}, datatype = float[8], order = C_order), Array(1..11, {(1) = 130.719, (2) = 231.20176000000004, (3) = 123.66, (4) = -17.275199999999998, (5) = .86334, (6) = 3.277899999999998, (7) = 995.475, (8) = 4.465, (9) = -2.402, (10) = 2.8765, (11) = .5000836}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = B(T), Y[2] = C(T), Y[3] = DD(T), Y[4] = E(T), Y[5] = F(T), Y[6] = G(T), Y[7] = H(T), Y[8] = J(T), Y[9] = K(T), Y[10] = L(T), Y[11] = M(T)]`; YP[1] := 100-0.594e-1*Y[1]+.7902*Y[6]+.11*Y[5]; YP[2] := 0.34e-1*Y[1]*Y[8]-0.75536e-1*Y[2]; YP[3] := 0.25e-1*Y[1]*Y[10]-0.34e-1*Y[4]-.8344*Y[3]; YP[4] := -.3954*Y[4]-0.25e-1*Y[2]; YP[5] := 0.136e-3*Y[2]-.1104*Y[5]+0.5145e-1*Y[4]; YP[6] := .7*Y[3]-.7906*Y[6]+.19355*Y[4]; YP[7] := 1000-0.905e-1*Y[7]; YP[8] := 0.9e-1*Y[7]-0.5e-3*Y[8]; YP[9] := .636-.1519*Y[9]; YP[10] := .15*Y[9]-0.19e-2*Y[10]; YP[11] := 0.1231e-1*Y[3]+0.14772e-2*Y[4]-0.5e-2*Y[11]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = B(T), Y[2] = C(T), Y[3] = DD(T), Y[4] = E(T), Y[5] = F(T), Y[6] = G(T), Y[7] = H(T), Y[8] = J(T), Y[9] = K(T), Y[10] = L(T), Y[11] = M(T)]`; YP[1] := 100-0.594e-1*Y[1]+.7902*Y[6]+.11*Y[5]; YP[2] := 0.34e-1*Y[1]*Y[8]-0.75536e-1*Y[2]; YP[3] := 0.25e-1*Y[1]*Y[10]-0.34e-1*Y[4]-.8344*Y[3]; YP[4] := -.3954*Y[4]-0.25e-1*Y[2]; YP[5] := 0.136e-3*Y[2]-.1104*Y[5]+0.5145e-1*Y[4]; YP[6] := .7*Y[3]-.7906*Y[6]+.19355*Y[4]; YP[7] := 1000-0.905e-1*Y[7]; YP[8] := 0.9e-1*Y[7]-0.5e-3*Y[8]; YP[9] := .636-.1519*Y[9]; YP[10] := .15*Y[9]-0.19e-2*Y[10]; YP[11] := 0.1231e-1*Y[3]+0.14772e-2*Y[4]-0.5e-2*Y[11]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..11, {(1) = 0., (2) = 100., (3) = 90., (4) = 45., (5) = 38., (6) = 10., (7) = 45., (8) = 50., (9) = 70., (10) = 20., (11) = 65.}); _vmap := array( 1 .. 11, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5), ( 6 ) = (6), ( 7 ) = (7), ( 9 ) = (9), ( 8 ) = (8), ( 11 ) = (11), ( 10 ) = (10)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [T, B(T), C(T), DD(T), E(T), F(T), G(T), H(T), J(T), K(T), L(T), M(T)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

 

 

 

 

 

 

 

 

 

 

 

 

 


 

Download odeStuff.mw

You still have 442 equations in 441 unknowns - this is not good!

For values of the loop variable T from 1..19, the equation system is over-deteremined and results are obtained

However for T=20, the equation system is inconsistent, and no answer is obtained. This is always a possibility if you have more equations than unknowns - you really should address this issue
 

restart

with(LinearAlgebra); interface(rtablesize = 10); interface(version); Physics:-Version()

`Standard Worksheet Interface, Maple 2019.0, Windows 7, March 9 2019 Build ID 1384062`

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple", `2019, April 26, 7:48 hours, version in the MapleCloud: 353, version installed in this computer: 350.`

(1)

Ne, Ng := 20, 20

20, 20

(2)

Lambda := 20; `&mu;e` := 20.0; `&mu;g` := 4; r := .35; rb := 1-r; c := 20.0; fe, fg := 100, 50

20

 

20.0

 

4

 

.35

 

20.0

(3)

Pne := proc (i) options operator, arrow; add(Pvals[i+1, j+1], j = 0 .. Ng) end proc; Ce := proc (n) options operator, arrow; fe+c*(n+1)/`&mu;e` end proc; Cg := fg+c/`&mu;g`+r*fe+r*add(i*Pne(i), i = 1 .. Ne); Wepc := proc (T) options operator, arrow; add(Lambda*Ce(n)*Pne(n), n = 0 .. T-1)+add(Lambda*Cg*Pne(n), n = T .. Ne) end proc; Sepc := proc (T) options operator, arrow; add(Lambda*(Ce(n)-fe)*Pne(n), n = 0 .. T-1)+add(Lambda*(-fe*r+Cg-fg)*Pne(n), n = T .. Ne) end proc; Eepc := proc (T) options operator, arrow; add(i*Pne(i), i = 1 .. Ne)/Lambda end proc

Warning, `j` is implicitly declared local to procedure `Pne`

 

Warning, `n` is implicitly declared local to procedure `Wepc`

 

Warning, `n` is implicitly declared local to procedure `Sepc`

 

Warning, `i` is implicitly declared local to procedure `Eepc`

 

for T to 20 do for i to Ne do if i <= T then Id[i] := 1 else Id[i] := 0 end if; if i = T then Idt[i] := 1 else Idt[i] := 0 end if end do; eqn[0, 0] := Lambda*P[0, 0] = `&mu;g`*rb*P[0, 1]+`&mu;e`*P[1, 0]; for j to Ng-1 do eqn[0, j] := (Lambda+`&mu;g`)*P[0, j] = `&mu;g`*rb*P[0, j+1]+`&mu;e`*P[1, j] end do; for i to Ne-1 do eqn[i, 0] := (Lambda+`&mu;e`)*P[i, 0] = `&mu;g`*r*P[i-1, 1]+`&mu;g`*rb*P[i, 1]+Lambda*Id[i]*P[i-1, 0]+`&mu;e`*P[i+1, 0] end do; for j to Ng-1 do for i to T do eqn[i, j] := (Lambda+`&mu;e`+`&mu;g`)*P[i, j] = `&mu;g`*r*P[i-1, j+1]+`&mu;g`*rb*P[i, j+1]+Lambda*Idt[i]*P[i, j-1]+`&mu;e`*P[i+1, j]+Lambda*P[i-1, j] end do; for i from T+1 to Ne-1 do eqn[i, j] := (Lambda+`&mu;e`+`&mu;g`)*P[i, j] = `&mu;g`*r*P[i-1, j+1]+`&mu;g`*rb*P[i, j+1]+`&mu;e`*P[i+1, j]+Lambda*P[i, j-1] end do end do; eqn[0, Ng] := (Lambda+`&mu;g`)*P[0, Ng] = `&mu;e`*P[1, Ng]; for i to T-1 do eqn[i, Ng] := (Lambda+`&mu;e`+`&mu;g`)*P[i, Ng] = `&mu;e`*P[i+1, Ng]+Lambda*P[i-1, Ng] end do; eqn[T, Ng] := (`&mu;e`+`&mu;g`)*P[T, Ng] = `&mu;e`*P[T+1, Ng]+Lambda*P[T, Ng-1]+Lambda*P[T-1, Ng]; for i from T+1 to Ne-1 do eqn[i, Ng] := (`&mu;e`+`&mu;g`)*P[i, Ng] = `&mu;e`*P[i+1, Ng]+Lambda*P[i, Ng-1] end do; eqn[Ne, 0] := (Lambda+`&mu;e`)*P[Ne, 0] = `&mu;g`*r*P[Ne-1, 1]+`&mu;g`*rb*P[Ne, 1]; for j to Ng-1 do eqn[Ne, j] := (`&mu;g`*rb+`&mu;e`+Lambda)*P[Ne, j] = `&mu;g`*r*P[Ne-1, j+1]+`&mu;g`*rb*P[Ne, j+1]+Lambda*P[Ne, j-1] end do; eqn[Ne, Ng] := (`&mu;g`*rb+`&mu;e`)*P[Ne, Ng] = Lambda*P[Ne, Ng-1]; Normeq1 := add(add(P[i, j], i = 0 .. Ne), j = 0 .. Ng) = 1; Eqns1 := {Normeq1, seq(seq(eqn[i, j], i = 0 .. Ne), j = 0 .. Ng)}; V := [indets(Eqns1)[]]; nops(V); AB := GenerateMatrix(Eqns1, V, augmented); Vsol := LinearSolve(AB); Pvals := Matrix(Ne+1, Ng+1, proc (i, j) options operator, arrow; Vsol[(i-1)*Ne+j] end proc); printf("\t\t%2d  %12.6f  %12.6f  %12.6f\n", T, Wepc(T), Sepc(T), Eepc(T)) end do

                 1   2596.382269    109.979252      0.071201

                 2   2347.352914     87.773894      0.093293

                 3   2209.802236     79.574841      0.113162

                 4   2128.374904     77.739266      0.132026

                 5   2091.079210     80.530239      0.152827

                 6   2080.591604     86.318160      0.176209

                 7   2082.494081     93.746266      0.201287

                 8   2089.809712    102.075779      0.227337

                 9   2099.606115    110.937241      0.253971

                10   2110.630201    120.135352      0.280999

                11   2122.315823    129.557807      0.308326

                12   2134.393489    139.134785      0.335907

                13   2146.730874    148.819930      0.363725

                14   2159.263490    158.580728      0.391779

                15   2171.962493    168.393234      0.420079

                16   2184.817282    178.238842      0.448642

                17   2197.803337    188.099994      0.477479

                18   2210.530367    197.924124      0.506389

                19   2217.107765    207.102047      0.531995

Error, (in LinearAlgebra:-LinearSolve) inconsistent system

 

numelems(Eqns1); numelems(V)

442

 

441

(4)

 

Download lSol.mw

is as shown in the attached - the main trick is to specify whether you want a matrix, vector or a table as the resulting type


 

  restart:

  with(LinearAlgebra):
  interface(version);
  Physics:-Version();
  interface(rtablesize=10):
  A:=  RandomMatrix(3);
  AA:= Matrix( op(1, A), (i,j)->A[i,j]/A[i,i]);
  B:=  RandomVector(3);
  BB:= Vector( op(1, B), i->B[i]/B[i]);

`Standard Worksheet Interface, Maple 2019.0, Windows 7, March 9 2019 Build ID 1384062`

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple", `2019, April 26, 7:48 hours, version in the MapleCloud: 352, version installed in this computer: 350.`

 

Matrix(3, 3, {(1, 1) = 33, (1, 2) = 57, (1, 3) = -76, (2, 1) = -98, (2, 2) = 27, (2, 3) = -72, (3, 1) = -77, (3, 2) = -93, (3, 3) = -2})

 

Matrix(3, 3, {(1, 1) = 1, (1, 2) = 19/11, (1, 3) = -76/33, (2, 1) = -98/27, (2, 2) = 1, (2, 3) = -8/3, (3, 1) = 77/2, (3, 2) = 93/2, (3, 3) = 1})

 

Vector(3, {(1) = -38, (2) = -18, (3) = 87})

 

Vector[column](%id = 18446744074376763262)

(1)

 


 

Download defMat.mw

 

Check out the attached


 

restart;

kernelopts(version);

`Maple 2017.3, X86 64 WINDOWS, Sep 13 2017, Build ID 1262472`

(1)

b := 120*Unit(mm);
h := 200*Unit(mm);
V := 8*Unit(kN);
I__x := 1/12*b*h^3;
Q := x -> simplify(1/2*(1/4*h^2 - (100*Unit(mm) - x*Unit(mm))^2)*b);
tau := x -> simplify(V*Q(x)/(I__x*b));
plot(Q(x), x = 0 .. 100);
plot(tau(x), x = 0 .. 100);

120*Units:-Unit(mm)

 

200*Units:-Unit(mm)

 

8*Units:-Unit(kN)

 

80000000*Units:-Unit(mm)^4

 

proc (x) options operator, arrow; simplify((1/2)*((1/4)*h^2-(100*Unit(mm)-x*Unit(mm))^2)*b) end proc

 

proc (x) options operator, arrow; simplify(V*Q(x)/(I__x*b)) end proc

 

 

 

 

 

 

 


 

Download plotUnits.mw

The attached code runs in Maple2019, Maple2018 and Maple 2017 and produces the same answer

No solution for the PDE is obtained in Maple2016, Maple2015 and Maple 18

  restart;

  interface(rtablesize=10):
  interface(version);
  Physics:-Version();
  assume(0 < x, 0 < y, y < 1, L > 0);
  interface(showassumed=0);

`Standard Worksheet Interface, Maple 2019.0, Windows 7, March 9 2019 Build ID 1384062`

 

"C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple", `2019, April 26, 7:48 hours, version in the MapleCloud: 352, version installed in this computer: 350.`

 

1

(1)

  pde := diff(f(x, y), x $ 2) + diff(f(x, y), y $ 2) = 0;

diff(diff(f(x, y), x), x)+diff(diff(f(x, y), y), y) = 0

(2)

  bcs := f(x, 0) = exp(-x), D[1](f)(0, y) = 0,
         D[2](f)(x, 1) = 0, f(L, y) = 0;

f(x, 0) = exp(-x), (D[1](f))(0, y) = 0, (D[2](f))(x, 1) = 0, f(L, y) = 0

(3)

  sol := pdsolve([pde, bcs]);

f(x, y) = Sum(2*cos((1/2)*(1+2*n)*Pi*x/L)*((-1)^n*Pi*(1/2+n)*exp(-L)+L)*(exp(-(1/2)*(1+2*n)*Pi*(y-2)/L)+exp((1/2)*(1+2*n)*Pi*y/L))/(((1/2+n)^2*Pi^2+L^2)*(exp((2*Pi*n+Pi)/L)+1)), n = 0 .. infinity)

(4)

``


 

Download pdeMaple2019.mw

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